Podcast
Questions and Answers
Which of the following options represents a well-defined set?
Which of the following options represents a well-defined set?
- All the honest members in the family
- All the prime numbers less than 100 (correct)
- All efficient doctors of a hospital
- All hardworking teachers in a school
Which set builder notation correctly represents the set {3, 9, 27, 81}?
Which set builder notation correctly represents the set {3, 9, 27, 81}?
- {x : x = 3^n, n ∈ N, n ≤ 4} (correct)
- {x : x = n^3, n ∈ N, n ≤ 4}
- {x : x = 3^n, n ∈ W, n < 5}
- {x : x = 3n, n ∈ N, n ≤ 4}
What is the roster form of the set {x : x ∈ W, x ≤ 5}, where W represents the set of whole numbers?
What is the roster form of the set {x : x ∈ W, x ≤ 5}, where W represents the set of whole numbers?
- {0, 1, 2, 3, 4, 5, 6}
- {0, 1, 2, 3, 4, 5} (correct)
- {1, 2, 3, 4, 5}
- {0, 1, 2, 3, 4}
Which of the following sets is an example of an empty set?
Which of the following sets is an example of an empty set?
Which of the following sets can be classified as a finite set?
Which of the following sets can be classified as a finite set?
Given the set A = {x | x ∈ N, and $x^2 - 3x + 2 = 0$}, determine the type of set A.
Given the set A = {x | x ∈ N, and $x^2 - 3x + 2 = 0$}, determine the type of set A.
Consider the set A = {x | x ∈ R, and $x^2 = 9, 2x = 4$}. What type of set is A?
Consider the set A = {x | x ∈ R, and $x^2 = 9, 2x = 4$}. What type of set is A?
Let A = {x : x is a letter in the word 'FOLLOW'} and B = {y : y is a letter in the word 'WOLF'}. How are the two sets related?
Let A = {x : x is a letter in the word 'FOLLOW'} and B = {y : y is a letter in the word 'WOLF'}. How are the two sets related?
Determine if the following pairs of sets are equal: A = {2} and B = {x : x ∈ N, x is an even prime number}.
Determine if the following pairs of sets are equal: A = {2} and B = {x : x ∈ N, x is an even prime number}.
Which of the following pairs represents equivalent sets?
Which of the following pairs represents equivalent sets?
Determine the cardinal number of set A = {x | x ∈ I, 2 < x < 7}, where I is the set of integers.
Determine the cardinal number of set A = {x | x ∈ I, 2 < x < 7}, where I is the set of integers.
Which of the following statements about sets is true?
Which of the following statements about sets is true?
What is the shortest possible way to write the set {2, 7, 7, 2, 3, 7, 8}?
What is the shortest possible way to write the set {2, 7, 7, 2, 3, 7, 8}?
Given A = set of natural numbers less than 8, B = {even natural numbers less than 12}, C = {Multiples of 3 between 5 and 15} and D = {Multiples of 4 greater than 6 and less than 20}, which of the following is equal to (B ∩ D) ∪ C?
Given A = set of natural numbers less than 8, B = {even natural numbers less than 12}, C = {Multiples of 3 between 5 and 15} and D = {Multiples of 4 greater than 6 and less than 20}, which of the following is equal to (B ∩ D) ∪ C?
Given A = {5, 7, 8, 9}, B = {3, 4, 5, 6}, and C = {2, 4, 6, 8, 10}, determine what is the value of n(B) + n(C) – n(B ∩ C), where n represents the number of distinct elements in a set.
Given A = {5, 7, 8, 9}, B = {3, 4, 5, 6}, and C = {2, 4, 6, 8, 10}, determine what is the value of n(B) + n(C) – n(B ∩ C), where n represents the number of distinct elements in a set.
What is the cardinal number of the set {x : x is a letter in the word ‘STATISTICS'}?
What is the cardinal number of the set {x : x is a letter in the word ‘STATISTICS'}?
Consider the set X = {letters of English alphabet up to 'h'} and Y = {all the vowels of English alphabet}. How would you describe the relationship by the Venn diagrams?
Consider the set X = {letters of English alphabet up to 'h'} and Y = {all the vowels of English alphabet}. How would you describe the relationship by the Venn diagrams?
If A and B are sets and A ∩ B = Ø, what can be concluded?
If A and B are sets and A ∩ B = Ø, what can be concluded?
If A is an empty set, what is the total number of elements in P(A), the power set of A?
If A is an empty set, what is the total number of elements in P(A), the power set of A?
Let A = {a, b, c} and B = {1, 2}. How many relations are possible from A into B?
Let A = {a, b, c} and B = {1, 2}. How many relations are possible from A into B?
Flashcards
Well-defined Set
Well-defined Set
A collection of items with clearly defined contents without ambiguity.
Empty Set (Null Set)
Empty Set (Null Set)
A set containing no elements; represented by {} or Ø.
Finite Set
Finite Set
A set with a finite number of elements.
Infinite Set
Infinite Set
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Singleton Set
Singleton Set
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Disjoint Sets
Disjoint Sets
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Equivalent Sets
Equivalent Sets
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Cardinal Number
Cardinal Number
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Subset
Subset
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Proper Subset
Proper Subset
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Reflexive Relation
Reflexive Relation
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Symmetric Relation
Symmetric Relation
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Transitive Relation
Transitive Relation
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Equivalence Relation
Equivalence Relation
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Injective Function
Injective Function
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Surjective Function
Surjective Function
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Bijective Function
Bijective Function
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Constant Function
Constant Function
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Identity Function
Identity Function
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Power Set
Power Set
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Study Notes
- These notes cover multiple-choice questions (MCQs) related to set theory.
Well-Defined Sets
- To be well-defined, a set's elements must have a clear criterion for membership.
- The colors in the rainbow are a well-defined set.
- Points on a straight line are a well-defined set.
- Prime numbers less than 100 are a well-defined set.
Set Builder Form
- A = {2, 4, 6, 8} can be written as {x : x = 2n, n ∈ N, 1 ≤ n ≤ 4}.
- B = {3, 9, 27, 81} can be written as {x : x = 3^n, n ∈ N, 1 ≤ n ≤ 4}.
- C = {1, 4, 9, 16, 25} can be written as {x : x = n², n ∈ N, 1 ≤ n ≤ 5}.
- D = {1, 3, 5, ...} can be written as {x : x = 2n - 1, n ∈ N}.
- E = {4, 6, 8, 9, 10, 12, 14, 15, 16, 18, 20, ... , 52} = {x : x ∈ N, x is composite, 4 ≤ x ≤ 52}.
- F = {-10, ... , -3, -2, -1, 0, 1, 2, ... , 5} can be written as {x : x ∈ Z, -10 ≤ x ≤ 5}.
- G = {0} can be written as {x : x = 0}.
- P = {} can be written as {x : x ≠x}.
Roster Form
- A = {x : x ∈ W, x ≤ 5} in roster form is {0, 1, 2, 3, 4, 5}.
- B = {x : x ∈ I, -3 < x < 3} in roster form is {-2, -1, 0, 1, 2}.
- C = {x : x is divisible by 12} in roster form is {..., -24, -12, 0, 12, 24, ...}.
- D = {x : x = 3p, p∈ W, p≤3} in roster form is {0, 3, 6, 9}.
- E = {x : x = a², a ∈ N, 3 < a < 7} in roster form is {16, 25, 36}.
- F = {x : x = n/(n + 1), n ∈ N and n ≤ 4} in roster form is {1/2, 2/3, 3/4, 4/5}.
Empty Sets
- Even natural numbers not divisible by 3 is not an empty set because 6, 12, 18 are examples.
- Prime numbers divisible by 2 is not an empty set because the number 2 is divisible by 2.
- {x : x ∈ N, 5 < x < 6} is an empty set because there are no natural numbers between 5 and 6.
- Odd natural numbers divisible by 2 is an empty set.
- P = {x: x is a prime number, 54 < x < 58} is an empty set.
- Q = {x : x = 2n + 3, n ∈ W, n ≤ 5} is not an empty set.
Finite and Infinite Sets
- The set of days in a week is a finite set.
- A = {x : x ∈ N, x > 1} is an infinite set.
- B = {x : x is an even prime number} is a finite set.
- D = {x : x is a factor of 30} is a finite set.
- P = {x : x ∈ Z, x < -1} is an infinite set.
Set Operations
- The set A={x, x∈N, and x²-3x+2 = 0} is a finite set.
- The set A={x, x∈R, and x²=9, 2x = 4} is a empty set.
- Let A= {x: x is a letter in the word FOLLOW}, B= {y: y is a letter in the word WOLF}, A≠B
- A = {2} and B = {x : x ∈ N, x is an even prime number} are equal sets
- The number of elements in set is known as a cardinal number.
- The domain & range are same for Identity function
- The set of all equivalence classes of a set A of cardinality C forms a partition of A
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